Note that the surface area of the prism is the sum of the surface areas of the 3 lateral faces and the 2 identical bases.
The bases are each right triangles with side lengths 9, and 12 cm. By the Pythagorean theorem we find that the length of the hypotenuse is:
[tex] \displaystyle{\sqrt{9^2+12^2}= \sqrt{81+144}= \sqrt{225}=15 [/tex] (cm).
(we can also notice that the triangle is the special case 3:4:5 multiplied by a factor of 3, so 9:12:15).
The surface area of each of the triangular bases is (1/2)*9*12=54 (square cm)
The lateral areas are each a rectangle of dimensions 10 by 9, 10 by 12, and 10 by 15.
Thus the total lateral area is 10*(9+12+15)=10*36=360 (square cm).
The total surface area is 2*54+360=108+360=436 (square cm)
Answer: 436 (square cm)
